As temperatures look set to hit 30c today, the council has asked people to look out for their neighbours.
Temperatures are likely to be high today and tomorrow before they drop slightly over the weekend.
The council said people should make sure they check on their neighbours, that vulnerable people should stay out of the sun between 11am and 3pm, wear sunglasses and sunscreen of at least SPF15, wear a hat, drink cool drinks, never leave anyone in a closed, parked vehicle and to keep living spaces cool by drawing the curtains while the sun is out and opening windows when the day cools down.
The heatwave can be especially difficult for Muslims observing Ramadan but the Muslin Council of Britain has advised that breaking the fast under heatwave conditions is allowable under Islamic law.
Anyone who is observing the fast is advised to drink water or another fluid if they feel dizzy, fain or disorientated.
Councillor Ruth Dombey, leader of the council, said: "It’s great to see the sun shining, but all of us need to make sure we’re taking steps to prevent heat-related illnesses and injuries.
"The simple ones are wearing high-protection sun cream, staying out of the sun during peak hours and drinking plenty of water. People also need to look out for their family, friends and neighbours during the warm weather and make sure they are keeping cool and have everything they need.
"Many people are enjoying the heat wave but these conditions can put the health of our elderly and vulnerable residents in jeopardy."
Safety tips are available on Sutton Council's website.